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hw10_sol_sp10

hw10_sol_sp10 - Physics 101 Classical Physics Spring 2010...

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Physics 101 Classical Physics Spring 2010 Homework 10 Solutions DUE IN CLASS ON April 15 1. If the frequency of a wave is 200 Hz, and the wavelength is 2 m, how much time is required for a single wave to pass by an observer? (a) 0.005 s , (b) 0.050 s, (c) 200 s, (d) 400 s, (e) 800 s Since the frequency is the number of wavelengths that pass a given point per unit time, the time for a single wave to pass an observer is 1 /f = 0 . 005 s. 2. If the frequency of a wave is 200 Hz, and the wavelength is 2 m, what is the velocity of the wave? (a) 0.05 m/s, (b) 0.50 m/s, (c) 200 m/s, (d) 400 m/s , (e) 800 m/s The velocity is given by the product of the frequency and wavelength v = = 400 m/s. 3. If the frequency of a wave is 200 Hz, and the velocity is 10 m/s, what is the wavelength? (a) 0.05 m , (b) 0.50 m, (c) 200 m, (d) 400 m, (e) 800 m Solving the relation used in problem 2 for the wavelength, λ = v/f = 0 . 05 m. 4. A transverse wave travels along a perfectly elastic string parallel to the ground. Any given point on the string: (a) doesn’t move (b) moves up and down (c) moves up only (d) moves left and right (e) depends on how high off the ground the string is. 5. A standing wave: (a) can be constructed from two similar waves traveling in opposite directions (b) must be transverse (c) must be longitudinal (d) has motionless points that are closer than half a wavelength (e) has a wave velocity that differs by a factor of two from what it would be for a traveling wave For example, the superposition of 2 waves travelling in opposite direction with the same frequency and amplitude can be written as A cos( kx - ωt ) + A cos( kx + ωt ) = 2 A cos( kx ) cos( ωt ) Then a given point at x executes simple harmonic motion, which gives a standing wave.

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